Orthogonal frequency division multiplexing (OFDM) modulates information symbols over a number of individual subcarriers. An OFDM signal includes multiple subcarriers modulated at different equi-spaced frequencies, which are orthogonal to each other. OFDM modulation is an effective modulation schema for transmission data at high rate over multipath fading channels. As an advantage, OFDM can be used in broadband digital communication applications because of its high spectral efficiency and robustness to the multipath fading channels. The IEEE 802.11 and IEEE 802.16 standards specify OFDM for high-speed wireless communications.
The IEEE standard 802.16-2004 defines two physical (PHY) layers called WirelessMAN-OFDM PHY and WirelessMAN-OFDMA PHY. The relevant portions of the standard include IEEE Std 802.16-2004, (Revision of IEEE Std 802.16-2001), IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems, and IEEE P802.16e draft/D9, IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems; Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands.
In OFDM, the available bandwidth in a channel is divided into N narrowband subcarrier frequencies, which are transmitted in parallel. The data are transmitted concurrently over these N equally spaced carriers. The subcarriers are designed to have a minimum frequency separation required to maintain the orthogonality of their corresponding waveforms. OFDM uses an inverse fast Fourier transform (IFFT) to generate the signal waveforms. The WirelessMAN-OFDM in the IEEE Std 802.16-2004 is based on 256 IFFTs. The OFDMA PHY mode in the IEEE P802.16e draft/D9 includes the IFFT sizes 2048, backward compatible to IEEE Std 802.16-2004), 1024, 512 and 128. One of the major drawbacks of OFDM is varying amplitude in the transmitted signal.
The constructive summation of N exponential signals can result in a peak power that is N times the average power. One of the frequently used measurements for the peak power is the peak-to-average power ratio (PAPR):
                              PAPR          =                                                                      max                                      0                    ≤                    t                    ≤                    NT                                                  ⁢                                                                                                x                      ⁡                                              (                        t                        )                                                                                                  2                                                            ave                ⁡                                  (                                                                                                          x                        ⁡                                                  (                          t                          )                                                                                                            2                                    )                                                      =                                                            max                                      0                    ≤                    t                    ≤                    NT                                                  ⁢                                                                                                x                      ⁡                                              (                        t                        )                                                                                                  2                                                                              1                  /                                      (                    NT                    )                                                  ⁢                                                      ∫                                          t                      =                      0                                        NT                                    ⁢                                                                                                                                      x                          ⁡                                                      (                            t                            )                                                                                                                      2                                        ⁢                                          ⅆ                      t                                                                                                          ,                            (        1        )            where x(t) is the OFDM transmitted signal, T is the sampling period, and N is the number of subcarriers for a OFDM symbol.
As the number of subcarriers in the OFDM signal increases, the amplitude of the OFDM signal becomes more like noise with a very large dynamic range. Therefore, the RF power amplifier (PA) in the transmitter should have a large input backoff, where the power conversion is inefficient. For example, the maximum power efficiency of a Class B PA is 78.5%. However, this efficiency drops to 7.85% for an input signal with a PAPR of 10 dB. Hence, the DC power consumption is 1.3 Watts to achieve a power level of 100 mW. The high DC consumption can decrease battery lifetime. Thus, a method for reducing the PAPR for OFDM signals is desired.
A number of different techniques are known.
Block encoding: A. E. Jones, T. A. Wilkinson and S. K. Barton, “Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes,” Electronics Letters, vol. 30, no. 25, pp. 2098-2099, December 1994. The codeword which reduces the PAPR is selected for transmission. There are some code sequences, for example, Shapiro-Rudin sequences, Golay codes, M-sequences, Binary Barker, and Newman phases, that have reduced PAPR. However, block encoding needs an exhaustive search for good codes. As N increases, this becomes impossible.
Selective mapping: R. W. Bäuml, R. F. H. Fisher and J. B. Huber, “Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,” Electronics Letters, vol. 32, no. 22, pp. 2056-2057, October 1996. The transmitter generates a set of candidate data blocks for the same information data block. The best mapping that has the lowest PAPR is selected for transmission. For implementation, the transmitter needs some IFFT operations, and determines the corresponding PAPR for these sequences. The side information of which candidate is used has to be transmitted with the information data block to the receivers. The complexity increases as the number of candidates increases.
Partial transmit sequences: S. H. Muller and J. B. Huber, “OFDM with reduced peak to average power ratio by optimum combination of partial transmit sequences,” Electronics Letters, vol. 33, no. 5, pp. 368-369 February 1997. The information data block of N symbols is partitioned into subblocks. The subcarriers in each subblock are weighted by a phase factor. The phase factors are selected such that the resulted PAPR is minimized. In general, the phase factors are limited to W elements to reduce the complexity. The side information of which phase factors is used is transmitted with the information data block to the receivers. The complexity increases as W increases.
Interleaving: P. V. Eetvelt, G. Wade and M. Tomlinson, “Peak to average power reduction for OFDM schemes by selective scrambling,” Electronics Letters, vol. 32, no. 21, pp. 1963-1964, October 1996. A set of interleavers is used to find the sequences having the minimum PAPR. The side information about which interleaver is used must be transmitted to the receivers. This method has the same problem for all the methods that need side information because an error in the side information can result in the lost of the transmitted signal.
Tone reservation and tone injection: J. Tellado, “Peak to average power reduction for multicarrier modulation,” Ph.D. dissertation, Stanford Univ., 2002. In one OFDM symbol, some subcarriers are reserved for PAPR reduction. The transmitted values for these subcarriers are determined by solving a convex optimization problem. The amount of PAPR reduction depends on the number of reserved subcarrier and their locations. For an IEEE 802.16 adaptive burst transmission, some subcarriers experiencing lower SNR can be used for this purpose. However, the subcarrier locations used for PAPR reduction should be changed adaptively. This leads to additional complexity. If the subcarrier locations are fixed, then bandwidth is reduced. Tone injection increases the size of a constellation such that each of the constellation points in the original constellation is mapped into several constellation points. Each transmitted symbol in the data block can be mapped into one of several equivalent constellation points. The problem with tone injection is that this technique can increase the power.
Peak windowing: M. Pauli and H. P. Kuchenbecker, “On the reduction of the out of band radiation of OFDM signals,” IEEE conference proceedings ICC, vol. 3, pp. 1304-1308, 1998. In this method, the PAPR is reduced by multiplying the large peak signal with a Gaussian window. PAPR reduction is achieved at the expense of out-of-band spectral components and in-band noise.
Companding: X. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Transactions on Broadcasting, vol. 45, no. 3, pp. 303-307, September 1999. This idea is similar to companding a speech signal. Because the OFDM signal is similar to speech in the sense that large peaks occur infrequently, a μ-law companding technique can be used to reduce the PAPR. However, companding also causes out-of-band spectral components, and symbol error rate improvement only occurs at higher SNR. The PAPR is reduced to approximately √{square root over (N)}.
Amplitude clipping and filter: X. Li and L. Cimini, “Effects of clipping and filtering on the performance of OFDM,” IEEE Communication Letters, vol. 2, no. 5, pp. 131-133, May 1998, and H. A. Suraweera, K. Panta, M. Feramez and J. Armstrong, “OFDM peak-to-average power reduction scheme with spectral masking,” Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP 2004), July 2004. Amplitude clipping limits the peak envelope of the input signal to a predetermined value. The noise caused by the non-linear properties of the clipping function falls both in-band (BER performance degradation) and out-of-band (spectral efficiency reduction). Filtering after the clipping can reduce the out-of-band noise. The most frequently used amplitude clipping operation is given by
                              x          n          ′                =                  {                                                                                          x                    n                                    ,                                                                                                                                            x                      n                                                                            <                  A                                                                                                                          A                    ⁢                                                                                  ⁢                                          ⅇ                                              jϕ                        n                                                                              ,                                                                                                                                            x                      n                                                                            ≥                  A                                                                                        (        2        )            where φn is the phase of xn and A is the pre-defined clipping level. This method is referred as hard clipping (HC). The masking of Suraweera et al. only removes a portion of the OOB radiation using hard clipping. They oversample by inserting many zeros in the transmitted signals in the frequency domain. This requires a very large value of the IDFT to generate the oversampled signal.
Most of the above techniques increase computational complexity and some of techniques decrease efficiency because side information is needed. Furthermore, there is another potential problem associated with techniques that need the side information. The error in the side information can result in the loss of whole transmitted signal.